1. Technical Field
The present invention relates to an electronic structure having a wiring pattern and method of designing the wiring pattern so as to control the temperature distribution in a portion of the wiring pattern.
2. Related Art
Electromigration due to an electric current in a conductive wire causes current-induced atomic diffusion due to momentum transfer from flowing electrons to host atoms, or a diffusion of electrons in electric fields set up in the wire while the circuit is in operation. Electromigration may cause connections at the end of the wire to degrade. For example, the interconnect may separate from an adjacent via, causing an opening or void in the circuit. In addition, metal at the end of the wire may form extrusions which may cause short-circuiting. Electromigration reliability is measured in terms of mean time to failure (MTF), which is defined as an increase in electrical resistance by a prescribed amount (e.g., 10%) for certain length and width interconnects at an assumed temperature with the application of a constant current density. The temperature may be in a range of 250 to 350° C., and the constant current density may be in a range of 20 to 30 mA/μm2.
Electromigration tests at the package-level are usually performed at a moderate current density (e.g., 20 to 30 mA/μm2) in an oven at a high temperature (e.g., 250 to 300° C.). Electronic structures in these package-level tests are stressed until they reach a certain failure criterion (e.g., 10 to 500 hours) such as a 10% increase in electrical resistance. In performing package-level tests, the time and cost to dice and package the wafers must also be taken into consideration. In these tests, the current density is small enough, so very little Joule heating occurs, eliminating the concern of temperature gradients. At the wafer level, however, Joule heating is used to raise the wire's temperature (e.g., 350-450° C.), which requires a very high current density (e.g., 400 mA/μm2). This method produces undesirable failure modes.
Accordingly, there is a need for an electronic structure having a multilayered substrate and a wiring pattern therein, together with an associated method of designing the wiring pattern, which avoids the undesirable failure modes for wires of the wiring pattern for an assumed current density.